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A company sells detergent in three different sized boxes: small (S), medium (M) and large (L). The medium size costs 50% more than the small size and contains 20% less detergent than the large size. The large size contains twice as much detergent as the small size and costs 30% more than the medium size. Rank the three sizes from best to worst buy.

$$\text{(A)}\, SML \qquad \text{(B)}\, LMS \qquad \text{(C)}\, MSL \qquad \text{(D)}\, LSM \qquad \text{(E)}\, MLS$$
Select the most appropriate letter.

Jan 23, 2019

#1
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Let the price of the small size = P   and let the quantity contained = Q

So....the unit price is     P /Q

Let the price of the meduim size =  1.5P

And let the quantity contained be   (2 - ..20)Q  =  1.8Q

So.....the unit price is    (1.5)P /  (1.8)Q   =  (5/6)P/Q

The large size price is (1.5)(1.3)P = 1.95 P

And the quantity is 2Q

So.....the unit price is  (1/95  P) / (  2Q)   =  (19/20)P/Q

So.....the best value from best to worst is

( 5/6)P/Q     (19/20)P/Q          P /Q  =

M                  L                      S   Jan 23, 2019
edited by CPhill  Jan 23, 2019